cos^2 30°+cos^2 60°+.......cos^2 180°=?

Explanation:

Another Explanation (5): প্রদত্ত রাশিমালাটি হল: \( cos^2 30° + cos^2 60° + cos^2 90° + cos^2 120° + cos^2 150° + cos^2 180° \) আমরা জানি, \( cos(180° - θ) = -cos(θ) \) সুতরাং, \( cos 120° = cos(180° - 60°) = -cos 60° \) \( cos 150° = cos(180° - 30°) = -cos 30° \) এখন, রাশিমালাটিকে লেখা যায়: \( cos^2 30° + cos^2 60° + cos^2 90° + (-cos 60°)^2 + (-cos 30°)^2 + cos^2 180° \) আমরা জানি, \( cos 30° = \frac{\sqrt{3}}{2} \) \( cos 60° = \frac{1}{2} \) \( cos 90° = 0 \) \( cos 180° = -1 \) সুতরাং, \( (\frac{\sqrt{3}}{2})^2 + (\frac{1}{2})^2 + 0^2 + (-\frac{1}{2})^2 + (-\frac{\sqrt{3}}{2})^2 + (-1)^2 \) \( = \frac{3}{4} + \frac{1}{4} + 0 + \frac{1}{4} + \frac{3}{4} + 1 \) \( = \frac{3}{4} + \frac{1}{4} + \frac{1}{4} + \frac{3}{4} + 1 \) \( = \frac{3+1+1+3}{4} + 1 \) \( = \frac{8}{4} + 1 \) \( = 2 + 1 \) \( = 3 \) অতএব, \( cos^2 30° + cos^2 60° + cos^2 90° + cos^2 120° + cos^2 150° + cos^2 180° = 3 \) সুতরাং, উত্তর 3 টি সঠিক। 🎉🥳